Cussons, Robert C.
A Unified and Microscopic Approach to Astrophysical Nuclear Reactions using Fermionic Molecular Dynamics.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2008)
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|Item Type:||Ph.D. Thesis|
|Title:||A Unified and Microscopic Approach to Astrophysical Nuclear Reactions using Fermionic Molecular Dynamics|
The aim of nuclear astrophysics is to understand the formation of the elements and the role played by nuclear reactions in the evolution of the universe, specifically by studying the complex interactions which occur on a microscopic scale between nuclei. To achieve this we must complement our understanding of how processes proceed on a quantum mechanical nuclear scale with observations made on an astrophysical scale, with the aim of improving our understanding of the universe in which we live. In this thesis a method will be described by which the astrophysical S-factor of radiative capture reactions can be calculated in a microscopic and unified way. Fermionic Molecular Dynamics (FMD) will be used to construct a non-orthogonal many-body basis out of explicitly antisymmetrised and angular momentum projected Slater determinants. The single particle basis states consist of gaussian wave packets which are localised in coordinate and momentum space and possess different widths. This provides an over-complete basis that can describe both scattering and bound states of nuclei. These serve as initial and final states, respectively, in the calculation of the transition matrix elements for electromagnetic transitions. By multiplying with the appropriate phase space factors, the cross section and hence the S-factor for radiative capture reactions can be calculated. In a microscopic description of nuclei an effective interaction between nucleons is required that is consistent with the chosen many-body basis. Realistic nucleon-nucleon potentials that perfectly describe the two-body phase shift data induce short-range correlations, which cannot be represented by the Slater determinants used in FMD. Therefore the Unitary Correlation Operator Method (UCOM) is employed to create an effective interaction that by construction delivers the same phase shifts as the realistic interaction. To formulate boundary conditions for the scattering states in the FMD basis the Collective Coordinate Representation (CCR) is used. This enables an operator to be defined that measures the relative distance between two well separated, completely antisymmetrised, many-body states. By matching to the known solution of the Coulomb problem for two point charges, the resonance energies and widths as well as the phase shifts can be calculated and compared with experimental data. Two radiative capture reactions which are of astrophysical interest are investigated: 3He(alpha,gamma)7Be and 14C(alpha,gamma)18O. The energy spectra of the compound nuclei are then compared with the experimental data for bound and resonant states. In the case of 3He(alpha,alpha)3He scattering, for which measurements of the elastic scattering phase shifts exist, comparisons are made to the calculations for both resonant and non-resonant channels. The agreement of the microscopic calculation with the experimental data is amazingly good considering that no use is made of an optical potential which has been fitted to the scattering data. The role of the nucleus-nucleus potential is fulfilled by the microscopic nucleon-nucleon interaction between the projectile and the target. For both reactions the astrophysical S-factor is calculated in separate partial waves at the low energies relevant for astrophysics for the chosen FMD model spaces. For the 3He(alpha,gamma)7Be reaction, this result is then compared with experimental data.
|Place of Publication:||Darmstadt|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 530 Physik
|Date Deposited:||14 Nov 2008 14:37|
|Last Modified:||07 Dec 2012 11:54|
|Referees:||Feldmeier, Prof Hans and Langanke, Prof Karlheinz|
|Refereed:||9 July 2008|